卷 76, 编号 3 (2021)

年: 2021
文章: 7
URL: https://journals.rcsi.science/0042-1316/issue/view/8354

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Convergence of Bieberbach polynomials: Keldysh's theorems and Mergelyan's conjecture

Aptekarev A.

摘要

Results due to Keldysh on the convergence of Bieberbach polynomials and the density of polynomials in spaces of analytic functions are considered. Their further development and relevance in the contemporary context of constructive complex analysis are discussed. Particular focus is placed on Mergelyan's conjecture on the rate of convergence in a domain with smooth boundary, which is still open.Bibliography: 20 titles.

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Uspekhi Matematicheskikh Nauk. 2021;76(3):3-12

3-12

(Rus)

(JATS XML)

Analytic moduli for parabolic Dulac germs

Mardešić P., Resman M.

摘要

This paper gives moduli of analytic classification for parabolic Dulac germs (that is, almost regular germs). Dulac germs appear as first return maps of hyperbolic polycycles. Their moduli are given by a sequence of Ecalle–Voronin-type germs of analytic diffeomorphisms. The result is stated in a broader class of parabolic generalized Dulac germs having power-logarithmic asymptotic expansions.Bibliography: 23 titles.

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Uspekhi Matematicheskikh Nauk. 2021;76(3):13-92

13-92

(Rus)

(JATS XML)

Equivariant minimal model program

Prokhorov Y.

摘要

The purpose of the survey is to systematize a vast amount of information about the minimal model program for varieties with group actions.We discuss the basic methods of the theory and give sketches of the proofs of some principal results.Bibliography: 243 titles.

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Uspekhi Matematicheskikh Nauk. 2021;76(3):93-182

93-182